Sobolev extension by linear operators

Charles L. Fefferman, Arie Israel, Garving K. Luli

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Let Lm,pn) be the Sobolev space of functions with mth derivatives lying in Lp(ℝn). Assume that n< p < ∞. For E ⊂ ℝn, let Lm,p(E) denote the space of restrictions to E of functions in Lm,pn). We show that there exists a bounded linear map T: Lm,p(E) → Lm,pn) such that, for any f ∈ Lm,p(E), we have Tf = f on E. We also give a formula for the order of magnitude of {norm of matrix}f{norm of matrix}Lm,p(E) for a given f: E → ℝ when E is finite.

Original languageEnglish (US)
Pages (from-to)69-145
Number of pages77
JournalJournal of the American Mathematical Society
Volume27
Issue number1
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Sobolev extension by linear operators'. Together they form a unique fingerprint.

Cite this